When it comes to feasability, you have to look at three things: location, labor, and the type of lair you are trying to build.
Location is the most important factor, because if it is in a remote area the construction can occur with minimal subtrifuge and interruption from locals (when I refer to locals I mean both civilians and government). It will also decrease your chances of the construction being seen by satellite surveilance. And, speaking of space, that type of lair is out of the question… it would take a huge number of launches to get the modules into orbit and that would definitley get noticed by the world's governments,
Labor is actually the biggest challenge, in that the more complex a lair the more skilled professionals and craftspeople you will need. If you want an ornate meeting room to taunt Bond in (like Dr. No had) you are going to have to hire people to lay the marble, to put in the raised ceiling, to emboss your super-villian logo in the wall… etc. For your control room you have to network the computers and servers together, you have to pipe in a high-speed data connection, you name it. You need air conditioning, you need plumbing… all this requires someone to do it. That's a lot of people, and you need to keep these people quite after they are done.
Contracting is kinda out of the question, as you can end up with dozens of guys in bars on Friday nights telling their buddies "Yeah, we just got threw with the SPECTRE job… man that Blofeld guy was a real stickler for detail." You could kill the workers when they are done, but that could draw unnecessary attention when dozens of men and women in a single area disappear. So you need to hire everyone, and keep them on the payroll (and potentially provide housing for them).
The type of lair is also important, in that burrowing out a volcano (for example) will take a huge amount of effort, equipment and materials that would definitely be noticable and take a HUGE amount of time. An "above ground" lair will take less work and can be disguised with a "cover" construction project that looks normal. I think a perfect location would be a new high-end hotel… you can set aside a dozen floors for your headquarters and your henchman can be disguised as hotel workers.
So, can an adversary of James Bond and MI6 build a huge cinematic hideout in real life? Yes, but I'd hate to be the project manager supervising the construction effort.